Uranium `._(92)U^(238)` decayed to `._(82)Pb^(206)`. They decay process is `._(92)U^(238) underset((x alpha, y beta))(rarr ._(82)Pb^(206))`
`t_(1//2)` of `U^(238) = 4.5 xx 10^(9)` years
Atomic mass of `U^(238)` is 238.125 amu. Its packing fraction will be

Options

A. 6.25
B. 0.125
C. 12.5
D. 5.25

Explanation

To find the packing fraction of Uranium-238, we can follow these steps:

### Step 1: Identify the isotopic weight of Uranium-238
The isotopic weight of Uranium-238 is given as 238.125 amu.

### Step 2: Identify the atomic weight of Uranium-238
The atomic weight of Uranium-238 is approximately 238 amu.

### Step 3: Calculate the packing fraction
The packing fraction is calculated using the formula:
\[ \text{Packing Fraction} = \frac{\text{Isotopic Weight} - \text{Atomic Weight}}{\text{Atomic Weight}} \times 10^4 \]

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ \text{Packing Fraction} = \frac{238.125 \, \text{amu} - 238 \, \text{amu}}{238 \, \text{amu}} \times 10^4 \]

### Step 5: Perform the subtraction
\[ 238.125 \, \text{amu} - 238 \, \text{amu} = 0.125 \, \text{amu} \]

### Step 6: Divide by the atomic weight
\[ \frac{0.125 \, \text{amu}}{238 \, \text{amu}} \approx 0.0005248 \]

### Step 7: Multiply by \(10^4\)
\[ 0.0005248 \times 10^4 = 5.248 \]

### Step 8: Round to appropriate significant figures
Rounding to three significant figures, we get:
\[ \text{Packing Fraction} \approx 5.25 \]

### Final Answer
The packing fraction of Uranium-238 is approximately **5.25**.

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